The CT-1024 did have built-in support backspace character. The key-switch on the KBD-5 keyboard was user defined. You could use the optional cursor control board to decode the backspace by the default SWTPC mapping did not allow that. A common hack was to piggy-back an IC on top of IC-30 on the main board and wire in this function.
The next generation terminal, the CT-64, decoded all control characters.
Here is the design for a small plug-in board that will decode the backspace and that can be wired to the cursor left function. The board can be removed with no damage to the unit. The design was done in ExpressPCB and here are the design files. Here are images of the schematic and board layout of the adapter.